Adding new object merges it with existing one
If you added a new mesh whilst in edit mode then the new mesh will become part of the object you're editing.  If you don't want this to be the case then you should add new meshes whilst in Object mode.  

If you've already added a mesh in Edit mode and you actually wanted those two meshes to be separate objects then you can do that with the Separate functionality.  Press P whilst in edit mode, and you should get a menu that allows you to separate the meshes.  Select "Loose parts" and you should now have two objects instead of one.  

This is documented in https://docs.blender.org/manual/en/latest/modeling/meshes/editing/misc.html